2013/03/13 by Bojana Femić, Femić, Bojana
Mathematics · #16T05 #18D10 #18D35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1303.3311
openalex publication_date 2013/03/13 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
With the motivation of giving a more precise estimation of the quantum Brauer\ngroup of a Hopf algebra H over a field k we construct an exact sequence\ncontaining the quantum Brauer group of a Hopf algebra in a certain braided\nmonoidal category. Let B be a Hopf algebra in C=H H YD, the category of\nYetter-Drinfel'd modules over H. We consider the quantum Brauer group\n BQ( C; B) of B in C, which is isomorphic to the usual quantum Brauer\ngroup BQ(k; B rtimes H) of the Radford biproduct Hopf algebra B rtimes H.\nWe show that under certain symmetricity condition on the braiding in C there\nis an inner action of the Hopf automorphism group of B on the former. We\nprove that the subgroup BM( C; B) - the Brauer group of module algebras over\nB in C - is invariant under this action for a family of Radford biproduct\nHopf algebras. The analogous invariance we study for BM(k; B rtimes H). We\napply our recent results on the latter group and generate a new subgroup of the\nquantum Brauer group of B rtimes H. In particular, we get new information on\nthe quantum Brauer groups of some known Hopf algebras.\n